Reinforced Concrete Design / module 6
Serviceability: cracking, deflection and durability
What the structure will actually be like to own. Unfactored loads, a cracked elastic section, and the two effects that decide whether a concrete floor is a success.
What you will understand
- Analyse a cracked section elastically and find its real stiffness
- Calculate the cracking moment and say what changes when it is passed
- Explain crack width as spacing times strain difference
- Use the span-to-depth rule, and say honestly what it is and is not
- Explain creep, and why it doubles or trebles a deflection
- Select cover from exposure and bond requirements
Lessons
The cracked elastic section
The state a beam spends its life in — and a different calculation entirely from the ultimate one.
Crack width and deflection
The two checks that decide whether a floor is a success — and the empirical rule that usually replaces one of them.
Module summary
- Serviceability uses UNFACTORED loads and a CRACKED ELASTIC section
- Cracking typically removes about two thirds of a beam's stiffness
- The neutral axis at service is much higher than at ultimate, and found differently
- Crack width = crack spacing × strain difference — the rest is empirical detail
- Bar SPACING controls cracking more than bar area does
- The span/depth rule is a screening device, not a deflection calculation
- Creep multiplies long-term deflection by two or three; it is a stiffness effect, not a strength one
- Cover is the greater of the bond and durability requirements, plus a deviation allowance
Teaching basis and review status
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesCheck your understanding
Check yourself
Which load combination should be used for a deflection check?
Practice
A 250 × 450 mm C30/37 beam. What is its cracking moment, in kNm? Take fctm = 2.90 N/mm².
Check yourself
Increasing cover from 30 mm to 50 mm for durability. What happens to the calculated crack width, all else equal?
Practice
A beam with Ig = 3.125 × 10⁹ mm⁴ has a cracked second moment of area of 1.13 × 10⁹ mm⁴. By what percentage does its flexural stiffness fall on cracking? Give the answer as a percentage.
Practice
An interior span of a continuous beam has d = 550 mm and a basic span/depth ratio of 14. What is its maximum span, in metres? Take K = 1.5.
Check yourself
What does a creep coefficient of φ = 2 mean physically?